Greenwood was born in Noranda, Quebec. He studied philosophy and economics at the University of British Columbia. He has been married to Susan Devlin since 1985; they have one child together.

Greenwood is a close friend of actor Gregg Henry, who appeared in Star Trek: Insurrection. Greenwood and Henry worked together on the NBC television movie The Great Pretender (filmed in 1989, aired in 1991). Years later, Greenwood urged Henry to begin recording the songs he was writing. Greenwood has provided vocals on all of Henry's CDs. [1]

Greenwood made his film debut in the 1979 adventure-thriller Bear Island. He then appeared in the first Rambo film, 1982's First Blood (composed by Jerry Goldsmith). His first major film roles were in the cult comedy The Malibu Bikini Shop (with Jay Robinson, Jon Rashad Kamal and Charlie Brill) and in the biographical adventure The Climb, both released in 1986.

He has worked with Egyptian director Atom Egoyan on three films: 1994's Exotica (with Victor Garber), 1997's The Sweet Hereafter, and 2002's Ararat. His work on The Sweet Hereafter earned him a nomination from the Genie Awards. One of his co-stars on Ararat was Star Trek VI: The Undiscovered Country's Christopher Plummer, whom he later worked with on The Summit.

Greenwood was nominated by the Genie Awards for his performance in the 2004 comic drama Being Julia. He then had a major role in the Academy Award-nominated Capote (2005), in which he played the title character's lover, Jack Dunphy. In this film, Greenwood co-starred with Clifton Collins, Jr., whom he again worked with on Star Trek. Greenwood, Collins, and the other principal cast members from Capote all shared a nomination from the Screen Actors Guild Awards for Outstanding Performance by a Cast in a Motion Picture.

Greenwood has acted in two films produced by Jerrry Bruckheimer: the 2006 time-travel drama Deja Vu (with Scott Klace and Scott Alan Smith) and 2007's National Treasure: Book of Secrets (which also featured Alicia Coppola and Larry Cedar). In the latter, Greenwood again played the role of a US President.

He worked with Steven Culp for a second time in the 2007 family comedy Firehouse Dog. Greenwood played a fictional character named Keenan Jones in the acclaimed 2007 semi-biographical drama I'm Not There, for which he, his cast members, and the film's casting directors won the Robert Altman Award from the Independent Spirit Awards.

Greenwood provided the voice of DC Comics' Bruce Wayne/Batman in the 2010 direct-to-video animated film Batman: Under the Red Hood. He voiced the same role in the television series Young Justice. This movie also featured the voices of Brian George, Dwight Schultz, and Wade Williams. Greenwood's Star Trek Into Darkness co-star, Peter Weller, also voiced Bruce Wayne/Batman in direct-to-video animated movies, namely Batman: The Dark Knight Returns, Part 1 (2012) and Batman: The Dark Knight Returns, Part 2 (2013).

Greenwood's other 2010 credits include the comedy Dinner for Schmucks (with Patrick Fischler), the comic drama Barney's Version (with Saul Rubinek) and the title role in the western Meek's Cutoff. The following year, he appeared as "Cooper" in the sci-fi mystery/thriller Super 8, which was written, produced and directed by Star Trek and Star Trek Into Darkness director-producer J.J. Abrams. "Cooper" was the on-set nickname for the CGI creature in the film; Greenwood performed the role through motion capture, providing the movements and facial expressions of the creature. [2] The film also featured appearances by Jason Brooks, Jonathan Dixon, Amanda Foreman, composer Michael Giacchino (who also scored the film), Tim Griffin, Tony Guma, and Marco Sanchez. Many of the creative staff involved with Star Trek and Star Trek Into Darkness also worked on Super 8, including producer Bryan Burk, casting directors April Webster and Alyssa Weisberg, film editors Maryann Brandon and Mary Jo Markey, and aforementioned composer Michael Giacchino.

Greenwood's more recent films have included the historical drama For Greater Glory: The True Story of Cristiada (2012, with Bruce McGill), the Academy Award-nominated drama Flight (2012), the acclaimed crime drama The Place Beyond the Pines (2013, with Harris Yulin), the comedy And Now a Word From Our Sponsor (2013), the crime drama Devil's Knot (2013, with Gary Weeks), the thriller WildLike (2013), and the thriller The Captive (2014).

Currently in production are the television movie Westside (2013), the romance Lost Luck (2013), and the drama Endless Love (2014).

Greenwood was previously a regular on the short-lived CBC series Huckleberry Finn and His Friends. In 1984, he starred in the short-lived NBC series Legman and made two appearances on the ABC series Jessie, starring Kate Mulgrew.

In the 1989 television movie Spy, Greenwood starred opposite Star Trek IV: The Voyage Home actress Catherine Hicks, who played his ex-wife. That same year, Greenwood also starred in the Holocaust-World War II television movie Pursuit (also known as Twist of Fate), where he played a Nazi SS officer who, after plastic surgery, was portrayed by his Star Trek co-star Ben Cross. Greenwood then assumed the role of the SS officer's son set twenty years later in the second half of the film. John Glover also starred in the film, playing a Holocaust victim turned Israeli intelligence officer.

Greenwood's work in the 1990 television movie The Little Kidnappers earned him a Gemini nomination as Best Performance by an Actor in a Supporting Role. In 1991, he appeared in two episodes of the Lifetime series Veronica Clare, on which Robert Beltran and Tony Plana were regulars. He followed this with a recurring role as Pierce Lawton on the CBS series Knots Landing.

He co-starred with Star Trek: Voyager actor Tim Russ and Voyager guest actress Virginia Madsen in the 1994 television movie Bitter Vengeance. He won a Gemini Award for Best Guest Performance in a Series by an Actor for his appearance in a 1994 episode of Road to Avonlea. During the 1995-96 TV season, Greenwood starred on the acclaimed, Emmy Award-nominated UPN series Nowhere Man, along with Megan Gallagher.

Greenwood had a role in the 2001 movie A Girl Thing, as did Scott Bakula and Brent Spiner. That same year, Greenwood starred in the drama Haven, for which he received a third Gemini Award nomination. In 2002, Greenwood co-starred with the aforementioned James Cromwell in the A&E television movie The Magnificent Ambersons. He then starred with Leslie Hope in the 2004 television movie Meltdown. He starred opposite Jim Beaver, Willie Garson and Matt Winston in the HBO series John from Cincinnati (2007) and worked alongside Stephen McHattie and Christopher Plummer in the 2008 Canadian mini-series The Summit. He more recently starred in the short-lived paranormal action-horror series The River, on which Leslie Hope and Daniel Zacapa was also a regular.